[FOM] The boundary of objective mathematics

Monroe Eskew meskew at math.uci.edu
Sat Mar 14 18:22:20 EDT 2009

On Fri, Mar 13, 2009 at 10:36 AM, Paul Budnik <paul at mtnmath.com> wrote:
> My position is finitism with respect to what exists. It is not finitism
> with respect to which questions are objectively meaningful.  I consider
> questions about an infinite number of recursively enumerable events to
> be human creations that can have immense practical value, but do not
> correspond to anything that exists physically or in some Platonic universe.

Perhaps then the CH would be trivially true in your point of view,
rather than "not objective."  CH states that for all x, if x is an
infinite set of reals, then x is countable or size continuum.  If
there are no infinite sets then this is trivially true.  Perhaps you
would accept the axiom system ZF - infinity, + "there are no infinite
sets."  V_\omega is a good model of this.  Then your position would
just be one of which mathematical statements are true/false, rather
than dealing with a separate notion of "objectivity."

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